Question

In figure 3.5 the small rectangle that represent the natural numbers seems to be sitting inside the bigger rectangle representing the whole numbers. What does this diagrammatical placing of two number sets represent, and how should one understand and explain this representation mathematically? Rectangles Whole Numbers 0, 1, 2, 3, 4, 5, 6.... answer. Natural / Counting Numbers 1, 2, 3, 4, 5, 6.... A​

Answer 1

The diagrammatic placing of the small rectangle representing the natural numbers inside the bigger rectangle representing the whole numbers represents the fact that the set of natural numbers is a subset of the set of whole numbers. This means that every natural number is also a whole number, but not every whole number is a natural number.

Mathematically, we can represent this relationship using set notation. We can define the set of natural numbers as N = {1, 2, 3, 4, 5, ...} and the set of whole numbers as W = {0, 1, 2, 3, 4, 5, ...}. We can then say that N is a subset of W, which is denoted as N ⊆ W. This means that every element of N is also an element of W, but there may be elements in W that are not in N.